"Hagel has criticized discussion of a military strike by either the U.S. or Israel against Iran. He also has backed efforts to bring Iran to the table for talks on future peace in Afghanistan. Some lawmakers have been troubled by his comments and actions on Israel, including his reference to the 'Jewish lobby' in the United States."

McConnell said any defense nominee must have "a full understanding of our close relationship with our Israeli allies, the Iranian threat, and the importance of having a robust military."

The comments were echoed by Sen. Lindsey Graham, R-S.C.

"This is an in-your-face nomination by the president to all of us who are supportive of Israel," Graham said on CNN's State of the Union. "I don't know what his management experience is regarding the Pentagon — little, if any, so I think it's an incredibly controversial choice."

But speaking on the same program, Sen. Dick Durbin, the No. 2 Democrat in the Senate, called Hagel "a serious candidate if the president chooses to name him."

Obama himself has defended Hagel from the criticism on NBC's Meet the Press last week, calling him "a patriot."